According to the mtg rules, permanents phase in or out before you untap your permanents. Is there a moment between phasing in and untapping when an opponent can try to destroy a permanent while you are still "tapped"?
No, players do not receive priority during the untap step, which is the first step of the turn, so no spells or abilities can resolve then:
502.3. No player receives priority during the untap step, so no spells can be cast or resolve and no abilities can be activated or resolve. [...]